Section Modulus calculation and optimization

REPORT FOR SECTION MODULUS CALCULATION AND OPTIMIZATION

Aim

To calculate section modulus of hood and optimize the design to have improved section modulus.

Section modulus:-

Section modulus is a direct measure of a strength of any cross sectional area of an object about an reference axis.

The formula of section modulus is given by,

S=I / Ymax

Where,
I = Moment of inertia (mm^4)
Y = Distance between neutral axes and outermost fiber (mm)

Steps to calculate section modulus:-

• Step 1:- Find location of centroid of given cross section.
• Step 2:- Find moment of inertia about neutral axis (INAINA)
• Step 3:- Find YmaxYmax from neutral axis.
• Step 4:- Find elastic section modulus using the formula provided above.

Moment of inertia is nothing but offering resistance against the moment, bending or twisting. So higher the moment of ineria higher will be its resistance to deform is higher.

 Moment of inertia:

 The moment of inertia, otherwise known as the mass moment of inertia, angular mass, second moment of mass, or most accurately, rotational inertia, of a rigid body, is a quantity that determines the torque needed for a desired angular acceleration about a rotational axis, akin to how mass determines the force needed for the desired acceleration. It depends on the body's mass distribution and the axis chosen, with larger moments requiring more torque to change the body's rate of rotation.

Sectional Modulus Calculation and Optimization:

Case 1:

Here the sectional modulus of hood design before optimization of Front Impact:

Length: Distance between neutral axes and outermost fiber (mm)

Distance between outermost end to another outermost end (d) = 876.49mm

Case 2: Optimized design 

Inorder to increase the sectional modulus, cross sectional area has to be increased. So here the optmized design:-

Table of Section Modulus Calaculation of Front Crash:

	Moment of Inertia (I) before Optimization in mm	Moment of Inertia (I) After Optimization in mm	Distance  (Y=d/2) in mm	Section Modulus before optimization (S1=I/Y) in mm	Section Modulus after optimization (S2=I/Y) in mm
Minimum	M1 = 1.775*10^6	M1 = 2.14*10^6	876.49/2  = 438.245	4050.246	4883.113
Maximum	M2 = 6.106*10^8	M2 = 7.213*10^8	438.245	1393.284*10^3	1645.883*10^3

Results: 

• After the calculations of the above 2 cases the section modulus of an S1(Minimum) and S2(Minimum) the difference is 832.87mm.
• After the calculations of the above 2 cases the section modulus of an S1(Maximum) and S2(Maximum) the difference is 252.60mm.
• The section modulus value of case 2 is higher than the case 1 for both Maximum & Minimum 
• As we increase the section area, the moment of inertia & section modulus increase which means strength and load material also increase. Which the moment of inertia directly proportional to the strength of the material.

Side Impact:

Case 1:

Here the sectional modulus of hood design before optimization of Side Impact:

Length: Distance between neutral axes and outermost fiber (mm)

 

Distance between outermost end to another outermost end (d) = 485.336mm

Case 2: Optimized design 

Inorder to increase the sectional modulus, cross sectional area has to be increased. So here the optmized design:-

Table of Section Modulus Calaculation of Side Crash:

	Moment of Inertia (I) before Optimization in mm	Moment of Inertia (I) After Optimization in mm	Distance  (Y=d/2) in mm	Section Modulus before optimization (S1=I/Y) in mm	Section Modulus after optimization (S2=I/Y) in mm
Minimum	M1 = 7.3*10^5	M1 = 8.768*10^5	485.336/2  =          242.668	3008.225	3613.167
Maximum	M2 = 1.201*10^8	M2 = 1.407*10^8	242.668	494.915*10^3	579.804*10^3

Results: 

• After the calculations of the above 2 cases the section modulus of an S1(Minimum) and S2(Minimum) the difference is 604.942mm.
• After the calculations of the above 2 cases the section modulus of an S1(Maximum) and S2(Maximum) the difference is 84.889mm.
• The section modulus value of case 2 is higher than the case 1 for both Maximum & Minimum
• As we increase the section area, the moment of inertia & section modulus increase which means strength and load material also increase. Which the moment of inertia directly proportional to the strength of the material.

Conclusion:

• Section Modulus of Hood of the car was calculated and optimized section modulus with some changes or optimization and found some better results.
• As we increase the section area, the moment of inertia & section modulus increase which means strength and load material also increase. Which the moment of inertia directly proportional to the strength of the material.